{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:19Z","timestamp":1753894399941,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We consider two-player games over graphs and give tight bounds on the memory\nsize of strategies ensuring safety objectives. More specifically, we show that\nthe minimal number of memory states of a strategy ensuring a safety objective\nis given by the size of the maximal antichain of left quotients with respect to\nlanguage inclusion. This result holds for all safety objectives without any\nregularity assumptions. We give several applications of this general principle.\nIn particular, we characterize the exact memory requirements for the opponent\nin generalized reachability games, and we prove the existence of positional\nstrategies in games with counters.<\/jats:p>","DOI":"10.46298\/lmcs-20(1:10)2024","type":"journal-article","created":{"date-parts":[[2024,2,9]],"date-time":"2024-02-09T10:43:08Z","timestamp":1707475388000},"source":"Crossref","is-referenced-by-count":0,"title":["Playing Safe, Ten Years Later"],"prefix":"10.46298","volume":"Volume 20, Issue 1","author":[{"given":"Thomas","family":"Colcombet","sequence":"first","affiliation":[]},{"given":"Nathana\u00ebl","family":"Fijalkow","sequence":"additional","affiliation":[]},{"given":"Florian","family":"Horn","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2024,1,29]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/12956\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/12956\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,9]],"date-time":"2024-02-09T10:43:14Z","timestamp":1707475394000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/10547"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,29]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-20(1:10)2024","relation":{"has-preprint":[{"id-type":"arxiv","id":"2212.12024v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2212.12024v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2212.12024","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2212.12024","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2024,1,29]]},"article-number":"10547"}}